Sure! Let's get started by filling in the table with the corresponding values for [tex]\(s(x) = -2x^2\)[/tex].
We will evaluate [tex]\(s(x)\)[/tex] for each value of [tex]\(x\)[/tex] given: [tex]\(-2\)[/tex], [tex]\(-1\)[/tex], [tex]\(0\)[/tex], [tex]\(1\)[/tex], and [tex]\(2\)[/tex].
Here is the table with the values filled in:
\begin{tabular}{|c|l|l|l|l|l|}
\hline
[tex]$x$[/tex] & -2 & -1 & 0 & 1 & 2 \\
\hline
[tex]$s(x)$[/tex] & -8 & -2 & 0 & -2 & -8 \\
\hline
\end{tabular}
To sketch the graph of [tex]\(s(x) = -2x^2\)[/tex], follow these steps:
1. Plot the Points: Using the table we filled, plot the following points on the coordinate plane:
- (-2, -8)
- (-1, -2)
- (0, 0)
- (1, -2)
- (2, -8)
2. Draw the Parabola: Since [tex]\(s(x) = -2x^2\)[/tex] is a quadratic equation, its graph will be a parabola. The coefficient of [tex]\(x^2\)[/tex] is negative, so the parabola opens downward.
Here is a sketch of the graph for [tex]\(s(x) = -2x^2\)[/tex]:
```
|
4 |
|
2 |
| `
0 ---+---+---+---+-- x
| ` ` `
-2 | ` `
-4 |
| ` `
-6 | ` `
| ` `
-8 | ` `
-10 +-------------------
-2 -1 0 1 2
```
Key Features of the Graph:
- The vertex of the parabola is at the origin (0, 0).
- The parabola is symmetric about the y-axis.
- The points we plotted help to outline the shape of the parabola.
This visual should give you a good idea of what the graph of [tex]\(s(x) = -2x^2\)[/tex] looks like.
